General David Petraeus has ordered all Nato troops under his command in Afghanistan to pursue the enemy relentlessly, but also stressed the need to "reduce civilian casualties to an absolute minimum".

By prioritising efforts to earn the trust of the Afghan people, the US general countered concerns that he would relax strict rules of engagement that have angered some troops, who say they put them at greater risk when fighting insurgents.

Addressing the 150,000 international soldiers, sailors and marines under his command as simply "team", Petraeus warns that the alliance "cannot kill or capture our way to victory".

The guidelines say: "Moreover, if we kill civilians or damage their property in the course of operations, we will create more enemies than our operations eliminate."

The general, who rose to prominence both as the architect of the "surge" strategy in Iraq and as author of the US army's official manual on counterinsurgency operations, re-emphasised many orders made by his predecessors David McKiernan and Stanley McChrystal.

They include requirements for soldiers to set up bases as close as possible to the Afghan civilians they are protecting, saying they cannot "commute to the fight". There are also warnings that patrols should be done on foot rather than in vehicles and that soldiers should take off their sunglasses when talking to Afghans.

But for all the emphasis on winning hearts and minds, Petraeus also signalled a new aggression in the fight against the Taliban, ordering troops to "pursue the enemy relentlessly".

While McChrystal's rules of engagement have not been altered, a rule on the use of air strikes against buildings has been clarified after a review revealed that many junior officers applied it too rigidly.

It requires extreme care to be used when air strikes or artillery fire are ordered on buildings where insurgents are fighting in order to avoid destroying houses or killing civilians who might be sheltering there. The clarification seeks to dispel the belief of lower-level commanders that such strikes on abandoned homes are completely forbidden.

In the guidelines Petraeus also ordered his subordinates to "fight the information war aggressively" by hanging "their barbaric actions like millstones around their necks", a move already reflected in Isaf's public communications.

And foreign soldiers will also be expected to play a greater role in helping crack down on corrupt government officials, including by bringing "networks of malign actors" – Nato code for ostensibly pro-government warlords – to the attention of superior officers.

British and Afghan army forces today made what the Ministry of Defence described as a "significant gain" by seizing the Taliban stronghold of Sayedebad in central Helmand province as part of an operation, codenamed Tor Shezada, to squeeze insurgents out of population centres.

The MoD announced that two British soldiers were killed in separate incidents in Afghanistan on Sunday.

A soldier from 1st Battalion Scots Guards was shot dead in the Lashkar Gah district of Helmand, and a marine from 40 Commando Royal Marines died in an explosion in the Sangin district.